September 21, 2010

Optimal committee size

This is a very interesting paper in view of my recent post on democracy. The authors address the issue of how many evaluators or judges a committee ought to have. Adding more judges of similar competence improves accuracy of evaluation, but comes at a cost. Moreover, the optimal committee size depends on the quality of the judges, with the counterintuitive finding that it decreases as the judges become worse.

The moral: it pays to gather many experts, but it doesn't pay to gather many fools.

Democracy can be viewed as a form of decision-making system by a very large committee of mediocre evaluators. From a cost-benefit perspective it's a rather big waste.

PLoS ONE 5(9): e12642. doi:10.1371/journal.pone.0012642

The Calculus of Committee Composition

Eric Libby, Leon Glass

Modern institutions face the recurring dilemma of designing accurate evaluation procedures in settings as diverse as academic selection committees, social policies, elections, and figure skating competitions. In particular, it is essential to determine both the number of evaluators and the method for combining their judgments. Previous work has focused on the latter issue, uncovering paradoxes that underscore the inherent difficulties. Yet the number of judges is an important consideration that is intimately connected with the methodology and the success of the evaluation. We address the question of the number of judges through a cost analysis that incorporates the accuracy of the evaluation method, the cost per judge, and the cost of an error in decision. We associate the optimal number of judges with the lowest cost and determine the optimal number of judges in several different scenarios. Through analytical and numerical studies, we show how the optimal number depends on the evaluation rule, the accuracy of the judges, the (cost per judge)/(cost per error) ratio. Paradoxically, we find that for a panel of judges of equal accuracy, the optimal panel size may be greater for judges with higher accuracy than for judges with lower accuracy. The development of any evaluation procedure requires knowledge about the accuracy of evaluation methods, the costs of judges, and the costs of errors. By determining the optimal number of judges, we highlight important connections between these quantities and uncover a paradox that we show to be a general feature of evaluation procedures. Ultimately, our work provides policy-makers with a simple and novel method to optimize evaluation procedures.

13 comments:

Many years ago, Peter Drucker opined that the maximum number of people a manager could supervise was 6. From 37 years of service on faculty committees, I would say that that is the maximum and optimum committee size, too.

Many years ago, Peter Drucker opined that the maximum number of people a manager could supervise was 6. From 37 years of service on faculty committees, I would say that that is the maximum and optimum committee size, too.

Cabinets and commissions are much more effective in their organization than parliaments and senates as they have much less members and are exclusively composed of people commissioned to do a certain task.

optimum = a small number of people chosen from the best of their professions

In a possible future meritocratic aristocracy, people from different professions should work together in order to achieve certain tasks and governance should be more flexible than in representative democracies.

Still, we have much to learn from ancient government systems. Some of these were apparently much more pragmatic and efficient than representative democracies. Representative democracies are full of redundant organs and procedures.

It used to be argued that only the hereditary landholders should be allowed to vote as the peasants were not "expert" enough to make good decisions. The result was that were decisions were made that were optimal for the few wealthy landholders. But not for the majority hereditary poor.

The same arguments were used to argue against women and people with darker-hued skin being allowed to vote. They were "obviously" inferior judges and disaster would surely follow if they were given the vote. Chaos and barabarism would follow if they ever attained power.

If a panel of architects were to judge a contest for a civic structure, then what you get is a building that architects admire, not the rest of the population who have to use and live in it. A great deal of ugly crap is lauded by architects, who are the only people who "understand" it.

The audience choice at a music contest or art contest is often very different from the "expert" choice. Are the experts right, or the people?

In the first and second world war many very poor decisions were made by people who were at that time judged to be the "experts". The inbred aristocracy, born and reared in military lore. Everyone was sure of their superiority, especially the working classes. It was the obvious stupidity, and blatant abandonment of the duty of care to the lower orders (of people), displayed in battle that arguably led to social change in Britain.

The "experts" choose who the "experts" are.

Dictatorship by committee is still dictatorship and will ultimately favour only the dictators.

Decision-making bodies typically expand over time until such point that a "working group" within them or outside them takes over the real work of setting the agenda. For instance, George Washington's 4 man Cabinet had more power than the current Cabinet of about 20.

The audience choice at a music contest or art contest is often very different from the "expert" choice. Are the experts right, or the people?

You bring up a very good point. Who is really an expert in something?

There are fields where this is really clear-cut, e.g., chess or civil engineering. There are other fields where it is not, e.g., painting.

How should experts or leaders "emerge"? One idea is to choose them democratically. The problem with that idea is that non-experts can't judge the competence of experts. Using your own example, the majority of people might consider an expert someone who likes the latest pop song, and not someone who has a deep understanding of counterpoint and harmony.

Another idea is to have experts choose their own. This is roughly the system used in academia, or medicine, or the law. To become a lawyer you need to graduate from a law school and pass a bar exam. Ultimately you are judged by other lawyers both in school and in the exam.

The problem with that idea is that sometimes expert communities "work" (e.g., the succession of physicist PhD's from the Renaissance to today are certainly an example of a successful expert community), and sometimes they don't (e.g., the succession of astrologers in the local "astrological society").

The trick is to create communities of experts in any field that "work", and are also shielded constitutionally by the temptation to be corrupted or to abuse their office for personal gain. There are many ideas about how this could be achieved, but that's a topic for another post.

I agree that something like governing a country is more open to corruption than most fields of expertise. So harsh legal measures against corruption are a sine qua non. But they should be regulated in a way that will not harm the efficiency and meritocratic operation of the government.

As someone who lives in a state with high degree of direct democracy, and who is active in groups seeking to replace representative democracy entirely with direct democracy, you will have to excuse me if I find you infatuation with aristocracy grossly naive. Experts" are often too "myopic" to be able to make high-quality, policy-based decisions. Moreover, they typically are blinded by their confidence and belief in their own superiority. The "best and the brightest” are the very people who brought the global economy to the brink of destruction after all, destroying millions of "little" peoples' lives and livelihoods in the process.

The problem with your idea of governance by experts is that there is no such thing as a true and unbiased meritocracy. As someone who is both a bar certified lawyer and a PhD in Anthropology here in the United States, I can assure that those who "excel" in academia and law owe less to their intelligence and merit, than they do to their skills at interpersonal politics and impressing snobs. And the funny thing about rule by elites, however they may be chosen, is that in the end it always devolves to rule for the benefit of elites. No thank you, I will stay with the flawed but much fairer democratic system. Most people are not fools, and when issues are presented divorced of party affiliations and rhetoric, the majority of people almost always make very wise decisions that are the fairest to all concerned.

The problem with your chess game was not that it was democratic decision making process, but that it was a forced consensus decision making process. crowd sourcing only works if each member is allowed to rigidly and steadfastly maintain his or her original position, so that the average of all positions can be chosen—this is diametrically opposed to consensual decision making where the outcome is a solution no one wanted, simply because it was the only one everyone could agree upon. After having spent a considerable time at WIPO watching consensus decision making in practice, I have come to the conclusion it is the most evil form of governance there is.

The "best and the brightest” are the very people who brought the global economy to the brink of destruction after all, destroying millions of "little" peoples' lives and livelihoods in the process.

That is not true. The global economy was brought down by politicians who carried out an economically infeasible policy of high spending/borrowing low taxation.

Politicians want to spend (because spending gets votes), they don't want to tax (because taxes lose votes). So, their optimal economic policy is to borrow, especially if this can be done cheaply (which it can, especially if you can print money).

The trouble is that borrowing catches up with you sooner or later, but politicians don't care about that as they are myopic in their electoral cycle thinking.

It is not the "experts" that ruined the global economy, but the unholy alliance of politicians (who want e.g., people to get houses) and the public (who want to benefit directly or indirectly from government spending).

Naturally, experts of a different sort, profited from the whole situation, but these were experts at exploiting a flawed system set up by politicians, not experts in economic governance.

The problem with your chess game was not that it was democratic decision making process, but that it was a forced consensus decision making process.

I think you misunderstand the rules of the game. Democracy is a forced consensus system, in which the people agree to obey by what the majority dictates.

crowd sourcing only works if each member is allowed to rigidly and steadfastly maintain his or her original position, so that the average of all positions can be chosen—this is diametrically opposed to consensual decision making where the outcome is a solution no one wanted, simply because it was the only one everyone could agree upon.

What's the average position of 50% "go to war" and 50% "not go to war"?

FWIW, court systems are generally organized according to this paradoxical principal.

The highest courts with, presumably, the most elite judges, tend to make decisions with the largest panels. Intermediate courts with judges of presumably intermediate expertise, tend to make decisions with medium sized panels. The least elite judges often rule their courts alone.

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